In recent years the formation of primordial galaxies, cosmic metal enrichment, and hydrogen reionisation have been studied using both refined observations and powerful numerical simulations. High-redshift quasars have become a ubiquitous tool in the study of this era with more than 115 quasars now spectroscopically confirmed at z>6.0. In this thesis, I use spectra of high-redshift quasars to provide improved observational constraints through a mixture of existing and new techniques. I first investigate the claim of neutral gas around the most distant known quasar, ULASJ1120+0641(J1120), with a cosmological redshift of z=7.1. Its spectrum shows a relatively weak Lyman-α emission line, which has been interpreted as evidence of absorption by neutral gas. Attributing this to a Gunn-Peterson damping wing has led to claims that the intergalactic medium is at least 10% neutral at that redshift. However, these claims rely on a reconstruction of the unabsorbed quasar emission. Initial attempts using composite spectra of lower-redshift quasars mismatched the CIV emission line of J1120, a feature known to correlate with Lyman-α and which is strongly blueshifted in J1120. I attempt to establish whether this mismatch could explain the apparently weak Lyman-α emission line. I find that among a C IV-matched sample the Lyman-α line of J1120 is not anomalous. This raises doubts as to the interpretation of absorbed Lyman-α emission lines in the context of reionisation. I then use a high quality X-Shooter spectrum of the same z=7 quasar to measure the abundances of diffuse metals within one billion years of the Big Bang. I measure the occurrence rates of CIV, CII, SiII, FeII and MgII, producing the first measurement at z>6 for many of these ions. I find that the incidence of CIV systems is consistent with a continuing decline in the total mass density of highly ionized metals, a trend seen at lower redshifts. The ratio CII/CIV, however, seems to remain constant or increase with redshift, in line with predictions from models which include a decline of the ionising ultraviolet background. The evolution in MgII appears somewhat more complex; while the number density of strong systems continues to decline at high redshift,the number density of weak systems remains high and may even increase. This could signal an increase with redshift in the cross-section of low-ionisation metals. Large numbers of weak MgII systems are also seen at z∼2, suggesting they were already in place when reionisation was ending. I use this X-Shooter spectrum to study metal absorbers associated with the z=7 quasar itself. I find that one such absorber shows signs of only partially covering the line-of-sight, and investigate the possible implications for the quasar’s environment. Finally, I investigate the evolution of the intergalactic medium’s Lyman-α opacity using spectra of quasars at 5.7<z<7.1. I assemble a sample of 92 quasar spectra, more than 3 times larger than previous samples.The sample consists of quasars drawn from DES-VHS, SDSS and SHELLQs, new reductions of archival data, and new data. I develop methods to quantify the opacity distribution, providing measurements of the distribution function up to z=6.1. I find that the Lyman-α opacity evolves strongly with redshift. The scatter may be even larger than previously appreciated, posing a serious challenge for models of reionisation.